Academic Journal
Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications
| Τίτλος: | Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications |
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| Συγγραφείς: | Hinds, Piers D., Sharma, Akash, 1994, Tretyakov, Michael V. |
| Πηγή: | Mathematical Models and Methods in Applied Sciences. 35(8):1845-1887 |
| Θεματικοί όροι: | consensus-based optimization, reflected stochastic differential equations, constrained sampling, reflected mean-field diffusion, mean-field Langevin dynamics, propagation of chaos, constrained optimization, Interacting particle system |
| Περιγραφή: | In this paper, we establish well-posedness of reflected McKean-Vlasov stochastic differential equations (SDEs) and their particle approximations in smooth non-convex domains. We prove convergence of the interacting particle system to the corresponding mean-field limit with the optimal rate of convergence. We motivate this study with applications to sampling and optimization in constrained domains by considering reflected mean-field Langevin SDEs for sampling and two reflected consensus-based optimization (CBO) models. We utilize reflection coupling to study long-time behavior of reflected mean-field SDEs and also investigate convergence of the reflected CBO models to the global minimum of a constrained optimization problem. We numerically test reflected CBO models on benchmark constrained optimization problems and an inverse problem. |
| Περιγραφή αρχείου: | electronic |
| Σύνδεσμος πρόσβασης: | https://research.chalmers.se/publication/546695 https://research.chalmers.se/publication/546695/file/546695_Fulltext.pdf |
| Βάση Δεδομένων: | SwePub |
| ISSN: | 02182025 17936314 |
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| DOI: | 10.1142/S0218202525500241 |